Numerous boxes of this type are known.
In particular U.S. Pat. Nos. 3,144,167 and 5,186,318 disclose boxes each having a sealing lip integrally formed with a cup containing the supply of substance, said lip extending away from the cup and the body of the box and then being curved at its periphery towards the body of the box so as to bear thereagainst.
There exists a need to further improve the hermetic sealing of makeup boxes in order to prevent solvents contained in the substance from evaporating, but without the means used for obtaining the looked-for sealing spoiling the appearance of the box or making it too expensive to manufacture.